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Sibirskii Zhurnal Industrial'noi Matematiki, 2022, Volume 25, Number 1, Pages 92–104
DOI: https://doi.org/10.33048/SIBJIM.2022.25.107
(Mi sjim1164)
 

This article is cited in 1 scientific paper (total in 1 paper)

Unsteady flow of Maxwell viscoelastic fluid near a critical point with countercurrent at the initial moment

N. P. Moshkinab

a Lavrent’ev Institute of Hydrodynamics, pr. Akad. Lavrentyeva 15, Novosibirsk 630090, Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
Full-text PDF (897 kB) Citations (1)
References:
Abstract: Two-dimensional unsteady stagnation-point flow of viscoelastic fluids is studied assuming that the fluid obeys the upper-convected Maxwell (UCM) model. The solutions of governing equations are found in assumptions that components of extra stress tensor are polynomials of spatial variable along solid wall. A class of solutions for unsteady flow in the neighbourhood of a front or rear stagnation point on a plane boundary is considered, and a range of possible behaviour is revealed, depending on an initial stage (initial data) and on whether the pressure gradient is accelerating or decelerating function of time. The velocity and stress tensor's components profiles are obtained by numerical integration the system of nonlinear ordinary differential equation. The solutions of equations exhibit finite-time singularities depending on the initial data and the type of pressure gradient dependence on time.
Keywords: unsteady critical point flow, Maxwell viscoelastic media, upper convective derivative, blow–up solution, Riccati equation. .
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00096
Received: 07.07.2021
Revised: 07.07.2021
Accepted: 13.01.2022
Document Type: Article
UDC: 532.135:532.5.013.2
Language: Russian
Citation: N. P. Moshkin, “Unsteady flow of Maxwell viscoelastic fluid near a critical point with countercurrent at the initial moment”, Sib. Zh. Ind. Mat., 25:1 (2022), 92–104
Citation in format AMSBIB
\Bibitem{Mos22}
\by N.~P.~Moshkin
\paper Unsteady flow of Maxwell viscoelastic fluid near a critical point
with countercurrent at the initial moment
\jour Sib. Zh. Ind. Mat.
\yr 2022
\vol 25
\issue 1
\pages 92--104
\mathnet{http://mi.mathnet.ru/sjim1164}
\crossref{https://doi.org/10.33048/SIBJIM.2022.25.107}
Linking options:
  • https://www.mathnet.ru/eng/sjim1164
  • https://www.mathnet.ru/eng/sjim/v25/i1/p92
  • This publication is cited in the following 1 articles:
    1. C. Chittam, S.V. Meleshko, “General solution of the Maxwell equations for the stagnation point problem with cylindrical symmetry for all values of the parameter in the Johnson-Segalman derivative”, Communications in Nonlinear Science and Numerical Simulation, 142 (2025), 108527  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский журнал индустриальной математики
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    Abstract page:163
    Full-text PDF :38
    References:60
    First page:9
     
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